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When is 1 the greatest common factor of 2 numbers?
1 is a factor of every whole number, and the gcf of two numbers can be 1 if there is no larger factor common to both numbers.
Why is the greatest common factor of two even numbers always even?
Even numbers, by definition, are divisible by 2. That means that every even number has at least one 2 as a factor. If every even number has one, then any set of even numbers will have at least one 2 as a common factor. Since that number has two as a factor, it's even.
What is a least common factor?
All numbers have factors. Some numbers have some of the same factors as other numbers. These are known as common factors. Since every number has 1 as a factor, 1 is always the least common factor of any set of integers.
Why are there greatest common factors and not least common factors?
1 is the least common factor of all whole numbers, so there is nothing to choose for a least common factor. The Greatest Common Factor (GCF) of a set of two or more numbers is the largest factor that will divide into every number in the set without leaving any remainder. 1 is the least, or smallest, factor common to all whole numbers.
Why you would never be asked to find the least common factor of a pair of numbers?
You would never be asked to find the least common factor of a pair of numbers because factors are the numbers that can be multiplied together to get a specific number, and the least common factor of any pair of numbers is always 1. This is because 1 is a factor of every number and is the smallest positive integer. Therefore, finding the least common factor of a pair of numbers would always result in 1, making it unnecessary to calculate.
What number is a common factor of every set of numbers why?
1
What is a common factor that every number has?
1 is the factor that is common to all numbers.
When is 1 the greatest common factor of 2 numbers?
1 is a factor of every whole number, and the gcf of two numbers can be 1 if there is no larger factor common to both numbers.
How you know that any two numbers have at least one common factor?
The number one is a factor of every number.
Which number is greatest factor of every number?
The greatest factor of any number is the number itself. There is no integer that is the greatest factor of every number. One is a factor of every number. One is the GCF of co-prime numbers.
Why is the gcf of any even number always even?
By definition, every even number has 2 as a factor. That means that every set of even numbers will have at least 2 as a common factor. The GCF might be higher, but if it has 2 as a factor, it's even.
Is it possible for two numbers to have no common factors?
No because every single number has a factor of one, therefore you have one as the common factor.
What is the least common factor of 3 and 6?
The least common factor of any set of numbers is 1.
Why is the least common factor of any two whole numbers is one?
The number one goes into every number making the the least (lowest) common factor.
What are numbers that have no common factors?
Since one is a factor of all non-zero integers, all numbers have common factors.
Is it possible for two numbers to not have a common factor?
No. Every set of numbers has 1 as a common factor.
Why is the greatest common factor of two even numbers always even?
Even numbers, by definition, are divisible by 2. That means that every even number has at least one 2 as a factor. If every even number has one, then any set of even numbers will have at least one 2 as a common factor. Since that number has two as a factor, it's even.
